In mathematical logic, Kalm�r proved that certain classes of formulas of the first order predicate calculus were Quine's . ) He discovered an alternative form of primitive recursive arithmetic, known as elementary recursive arithmetic, based on primitive functions that differ from the usual kind.
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Thus, natural language statements of the forms " All A is B, No A is B ", " Some A is B ", and " Some A is not B " can be represented in first order predicate calculus in which any existential import with respect to terms A and / or B is either explicit or not made at all.
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